The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  0  1  X  X  0  0  1  1  1  X  1  1  1  X  1
 0  X  0 X^2+X  0 X^2+X  0 X^2+X X^2 X^2+X  0 X^2+X  X X^2+X X^2+X X^2+X  X  X  0  0 X^2+X X^2+X X^2+X X^2+X  0  0 X^2
 0  0 X^2  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2
 0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0
 0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0
 0  0  0  0  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0
 0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2

generates a code of length 27 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+34x^20+30x^21+56x^22+78x^23+147x^24+246x^25+287x^26+326x^27+278x^28+218x^29+130x^30+106x^31+43x^32+18x^33+32x^34+2x^35+8x^36+6x^38+1x^40+1x^42

The gray image is a linear code over GF(2) with n=108, k=11 and d=40.
This code was found by Heurico 1.16 in 0.0992 seconds.